Transcript for NASA Connect - Geometry of Exploration - Eyes Over Mars


[inaudible] in the
science guy here.

When you dream about going places,
what is your mind taking somewhere

on earth or to the stars?

If you spend time looking

at the stars you'll notice
one there is a bit red.

It's actually not a star off the
planet Mars it's the next place

humans are going to
explore, of course none

of these exploration could be done
without science and mathematics.

On this episode of NASA Connect,

NASA will show you how the
principles of geometry are used

to survey and map our planet
earth and the planet Mars.

So hang tight as Van, Jennifer and
the NASA science guys survey earth

and Mars on this episode
of NASA Connect.

[ Music ]

[Jennifer:] Hey guys
welcome to NASA connect,

the show that connects
you to the world of math,

science, technology and NASA.

I am Jennifer Pulley.

[Van:] And I am Van Hughes.

Today we are here at the
Virginia Living Museum

in New Port East Virginia.

And right now we are
standing on a sundial

which is basically
a plate marked with

[inaudible] is a raised projection
that casts a shadow from the sun.

Jennifer why don't you come


According to your shadow
it's time to start the show.

[Jennifer:] Well Van this is
you know, bad way to tell time

but you I think I
rather use my watch.

You know through our
history the sun

and stars governed people's
days, years and even their lives.

Using sundials and observing
shadow was one way ancient people

told time.

Get this, you can even
measure height and distance

with shadows passed from the sun.

[Van:] In fact you can even
measure the circumference

of an entire planet like also
earth and or mars and something

as simple as a shadow.

[Jennifer:] And geometry, on today
NASA Connect we will examine how

NASA researchers use the principles
of geometry to survey the world

around us and the world beyond us.

[Van:] We will focus of
telescope to see how geometry

and satellites are used to measure,

map and survey other
planets like mars.

[Jennifer:] Which by the way can be
seen quite well in the planetarium?

Anyway we will visit some students
from George Washington University

who are studying and
surveying the martial landscape

at NASA Langley Research
Centre in Hampton Virginia.

[Van:] And we will
visit a researcher

from NASA's Jet Propulsion
Laboratory in Pasadena, California.

Who will show us how geometry is
used by NASA's Mars global survey.

Later on in this show students
from Central Middle School

and Charlotte Courthouse
Virginia will join us.

They have got now some
experiment they want to try.

[Jennifer:] Plus NASA's educational
technology program manager Dr.

[inaudible] will introduce
that to some students

from Davis Middle school
in Hampton Virginia.

These students are
using the internet

to create their own Mars
surveyor to learn more

about this web based
activity later in the show.

[Van:] Hey as we go to the show our
friend Norbert will visit you too.

Every time he appears with a
Q-card that's your Q to think

about the answers to the
questions he gives you.

Got it?

[Jennifer:] Plus we will go
to NASA Ames Research Centre

in Mountain View California
there we'll get all the latest

information on research for life
on Mars and learn all about.



[Jennifer:] So hand tight
as NASA Connect takes you

on a global surveyor mission
to our planet earth and -- -

>> Well it's surveying.

>> How to survey measures geometry?

>> Surveying is the measurement
of angles and distances,

elevation and direction.

This is especially
useful for locating

[inaudible] boundaries,
construction layout and map making.

>> Okay, Terry, can you tell me
how surveyors use this equipment

and geometry to survey land?

[Terry]: Yeah, just look at this
transit that contains a telescope,

a compass and a protractor
and is used

in major horizontal
and vertical angles.

You can measure angles in the field

with this they measure
those same angles

[inaudible] with a protractor.

The first one is used to layout
objects like football fields,

baseball fields, soccer fields.

Today let's demonstrate
how we use this by laying

out this football field.

>>: Alright.

[Terry]: First we take a
starting point inside the transit

over to the point.

We call this point
corner number one,

then we measure three hundred
feet to the next corner

and call it corner number four.

We mark this corner
with the colon mark.

With zero on the scale we
look through the telescope

and lineup corner number four.

We noted the angle
between the sides

of the rectangle is ninety degrees.

So we turned the telescope
towards corner number two

until we can read ninety degrees
on the transit circle or scale.

Now we measured the width of
the football field, one hundred

and fifty feet and more corner
number two, next we move to transit

over corner number two with
zero on the scale we look

through the telescope at
corner number one marker.

Return the telescope
towards corner number three

until we can read ninety
degrees on the scale.

We measure three hundred feet
in north corner number three.

You now have all of
the corners north,

applying one of the basic rules
of geometry, we noted the sum

of the interior angles of the four
sided polygon is three hundred

and sixty degrees.

So our last angle must
measure ninety degrees

for a correct layout.

The rule for checking the angles
of any object is that the sum

of the interior angles of
the close polygon is equal

to the number of side minus two
as one hundred ninety degree.

You know Jennifer the olden
science of survey had been used

for over 3400 years
in map and measure


Today, scientist at NASA
of the preventive measure

and map the planets
of our solar system.

[Jennifer:] Who knows,
maybe one day,

one of you will help survey Mars.

>> Did you know that George
Washington was a surveyor,

before he became President?

Did you know

[inaudible] on the
expression mission?

>> To understand angles
and circumference,

let's look at something we
can all relate to pizza.

Take the slice of pizza, can
you tell, just by looking at it,

how many slices were
in the original pizza

and how we around it was?

Sure you can, all it takes
is a little geometry.

A pizza usually has eight
identical slices, but not all.

Oh, so let's measure the
angle with of the slice.

That's a part you put
in your mouth first.

Excuse me sir.

What is this protractor read?

>> The protractor reads an
angle with forty five degrees.

>> Right, so what
is the measurement

of all the other angles
touching the center?

>> They have to be equal

or the same measurement
forty five degrees.

>> Right, now most
pieces are circular

and circles measures three
hundred and sixty degrees.

If you divide, three hundred sixty
degrees by forty five degrees,

the original pizza
had eight slices.

Now let's review the
circumference of this pizza.

Most pizzas are measured in
inches, so using the pizza

with eight slices, if the
links of the crust arc is five

and a half inches how
round is your pizza?

[Child:] If there eight slices

and the crust arc measures five
point five inches long then eight

and five point five inches
equals to forty four inches?

The Pizza has circumference
of forty-four inches!

>> Great! Try this one.

What if the angle width of your
Pizza slice measures thirty degree

and the crust arc is
two and a half inches.

How may slices would there
be in the original pizza

and what is the circumference?

[Child:] I've got it, three
hundred and fifty degrees divided

by thirty degrees
equals twelve slices.

Twelve slices times
two point five inches

because of circumference
of thirty inches.

>> So, Sir, would you rather
read out twelve slice pizza

or an eight slice pizza?

>> I'll choose the eight slices
as I couldn't possibly eat twelve.

>> Did you know that over 2000
years ago a Greek librarian use

geometry to determine the
circumference of the earth.


[inaudible] circumference
of the earth,

what are the angle relationship

between parallel lines
and a transversal?

>> The concept of the earth being
a large sphere was not unknown

to the ancient Greeks.

And everyday observations
such as the disappearance

of ships below the
horizon indicated

that the earth might
be spherical or round.

But how large was it?

The person who figured it
out was a librarian named

[inaudible] who lived in Alexandria
Egypt about 300 B.C. While looking

to a scroll one day he read
that at noon on the longest day

of the year, a vertical
column cast no shadow in

[inaudible] a city
south of Alexandria.

[inaudible] knew that this
did not happen in Alexandria.

He talked to himself, how was
it possible to have shadows

in Alexandria and not in

[inaudible] at the
same time of day?

[inaudible] figured out that the
sun must be directly overhead in

[inaudible] but not in Alexandria.

Aha! here was proved that the
earth's surface is curved.

Using a little geometry

[inaudible] set out to determine
the circumference of the earth

and find out just how big it is.

>> Just like our pizza
example if our friend

[inaudible] could determine
the central angle at the center

of the earth and the length of the
edge or arc then he could figure

out the circumference of the earth.

Now, finding the length of the
edge or arc was fairly simple math.

[inaudible] asked a friend
to walk from Alexandria to

[inaudible] to measure the
distance between the two cities.

His friend estimated
the distance to be

around eight hundred kilometers
or about five hundred miles.

Finding the central angle
however will take some geometry.


[inaudible] assumed correctly
that the sun's rays are parallel.

Since the sun is so far
away check this out.

In this diagram, we can see
that there is no shadow at

[inaudible] while there
is a shadow in Alexandria.

The line that is formed by
the no mark or vertical column

at Alexandria and the
centre of the earth cuts

or intersects the two parallel
lines formed from the sun's rays.

A line that intersects two parallel
lines is called a transversal.

The two angles formed
from the transversal line

and the parallel lines are
called alternate interior angles.

And according to geometric rule
they are equal, let's prove it.

Take a piece of paper of any width
and draw a diagonal line on it.

Label the angles A
and B just like this.

Now cut the paper
along the diagonals

so you have two triangles.

Compare angles A and B by placing
one angle on top of the other.

Hey, what do you notice?

[Child:] The angles are equals

in no matter what side
paper you started with.

>> Right! When two parallel lines
are intersected by a transversal,

the alternate interior
angles are equal.

[inaudible] who is
quite a geometer.

From his measurements, Aristophanes
calculated the suns rays made an

angle of seven and a half
degrees at Alexandria.

Now since this angle was
formed by two parallel lines

and a transversal the central angle

of the earth must also be
seven and a half degrees.

By knowing these two
things the central angle

and the distance from

[inaudible] calculated
circumference of the earth.

Three hundred sixty
degrees divided by seven

and a half degrees equals forty
eight slices of the earth.

Are you still with me, okay,
hang tight we are almost there.

Now if you remember that
the estimated distance

between Alexandria and Seine
is eight hundred kilometers

and you multiply that distance by
the number of slices in the earth.

Forty eight, what is the
circumference of the earth?

Well, if you estimated
that distance

to be thirty eight
thousand kilometers,

you are absolutely right.

[inaudible] estimate was really
close to the earth's circumference

which is forty thousand
seventy four kilometers.

This percentage air was about
five percent and was probably due

to an error in the distance
between the two cities.

Five percent, that's
pretty good considering

[inaudible] used only his
feet, his eyes, his imagination

and of course his
knowledge of geometry.

>> There are other ways that
we survey the earth which

[inaudible] never dreamed of.

NASA scientists use aero
planes and satellites.

>> But what if you want to
survey other planets like Mars.

>> NASA scientists are doing
that right now, but first.

Let's have the Central
Middle School

in Charlotte Court house Virginia

where students are following
in the foot steps of


>> Hi, welcome to
Central Middle school

in Charlotte, Court House Virginia.

>> NASA Connect asked us to
show how did the stage activity

for the show.

>> In this lesson you
work in small groups

to take accurate measurements
of shadows using geometry

to determine the size of an angle.

Here are the materials you
will need for each group.

A straight take of approximately
ninety one centimeters long.

[inaudible] a piece of strain
approximately ninety one

centimeters and


A scientific calculator index hard.

Compass, copies of the
student data chart

[inaudible] Lets begin, divide
the class in research groups

of three to five members.

Set your measurement
station by first placing the


For your measurement to be accurate
and it's critical vertical.

To check the vertical
position tie the rock or

[inaudible] to the string and


Next, measured the height of

[inaudible] place an index
card under the station to mark

where the shadow is,

take measurements every
two minutes beginning

at least ten minutes
before local noon.

When this is a time that
we sanitized in the sky.

This we most likely not in you,

as indicated on your
time measuring device.

Students should know that
when the sun is highest

in the sky the shadow
length is the shortest.

Since the edge of the shadow is
fussy and the shadow is moving

from east to west in Northern
Hemisphere, be careful in deciding

where to question mark.

Record your data on data chart one.

Now back in your classroom
locate the latitude and longitude

of your school location and
reported on dated chart number one.

Identify your best shadow link.

This is the best shadow
link at local noon time.

Next calculate the

[inaudible] by dividing the length
of the shadow by the height of the


Locate this number

[inaudible] round the
number on the tent of table.

The measure at the

[inaudible] can also be found by
the dividing the length of a shadow

by the height of an object
on the scientific calculator.

Record T&J or student data chart.

Make a scale drawing of

[inaudible] and shadow,
complete the triangle

and measure the tangent
with the protector

to verify the calculations.

What's next Jennifer?

[Jennifer:] Let's analyze the
data by reviewing the results

of this activity and by responding
to the following questions?

Did the weather conditions effect
the results of this activity?

If so how?

As the shadow lengthens overtime,
how would be angle be affected?

If each group uses a

[inaudible] with a
different length,

how would that affect the
results of this activity?

For more activities like
this, check out our website


>> NASA connect would like to
the special thanks to the mentors

from the AIAA Chapter at Howard
University in Washington DC.

We appreciate all your help
to the student activity.

>> Okay, let's review.

We have seen how the
sun's position satellites

and geometry help
us survey the earth,

but what if we wanted
to survey Mars?

>> Well we don't live on
Mars so how do scientist

and NASA survey the red planet.

>> I thought you've never asked.

Let's visit NASA's Jet
Propulsion Laboratory

in Pasadena California
and find out.

>> What is the Mar global
surveyor and where is it?

>> How does the Mars global
surveyor use geometry

to survey the Mars landscape?

>> Mars global surveyor is a space
craft that is in orbit around Mars.

Its purpose is to take pictures
of Mars, measure the temperature

of the surface and
the atmosphere of Mars

and to pass laser signals
off the surface of Mars

to precisely determine
the shape of Mars.

You might think of Mars as
simply being a sphere by looking

at pictures of it,
but the scientist

that it has lots of
bumps and bridges.

For example, the poles
of Mars are so cold

that the atmosphere actually
condenses out to form dry ice

at the pole and as much
as twenty five percent

of the atmosphere condenses out
in to the drier aside the pole.

So there is quite a lot of
change in the atmosphere.

Also Mars is known for having a
large poles on the side of it,

the largest volcano in the solar
system known as a Olympus Mars.

And so one of the functions of
the Mars global surveyor was

to measure the shape of Mars

to carefully determine
how big is this bulge.

It has a huge effect on the
orbits of space craft it's just

such a large bulge on the side.

The way that we use geometry
to convert the laser pulses

into the shape of Mars what we
have to do is carefully time,

I want to tick for the
pulses to reach mars

and bounce back to the space craft.

And then we combine that
with the shape of the orbit

which we determine by looking
at how the radio signal changes

as the space craft
goes around Mars.

>> What is aero breaking?

How does geometry
influence aero breaking?

>> Aero breaking is when we
use drag from the atmosphere

to gradually shrink the orbit down.

So what we have to do is use
the drag from the atmosphere

to gradually slow the orbit
down so that it would shrink

from this highly electrical
forty five hour orbit

down to a very circular
two hour orbit around Mars.

This is geometry inaction.

[Jennifer:] How when you
like to try your hand

at design your own
Mars global surveyor.

Before introducing you to
our featured ad tech activity

in Middle school, I want to give
you a quick tour of Norbert's lab.

You already know Norbert.

In fact when you care to the
providers with the Q-cards

and other going activities in

[inaudible] to help us
understand with the math, science

and technology concepts
presented in each

of the NASA Connect programs.

His lab is your interactive
length to activities and resources

on the web, so you will get
the most out of NASA Connect.

Just click on the rooms to
enter areas like courier corner

where you need some of our guest
and numbers of our television team.

There is a study room, with terms
and definitions related to the show

and a page with links to
other cool sites and this is

where you will get to the online
activity especially created

in partnership with NASA's
running technologies team.

To introduce us to the web activity

for this show let's
pop in on a teacher

[inaudible] Davis Middle
school in Hampton Virginia.

[Viviane:] Thanks
Jelly, my name Viviane


I am a math and science teacher
here at Davis Middle School.

My students love coming
to the computer lab.

They used up a reinforcement
and enrichment of many skill

at most of the content areas.

Now I would like to
introduced to the


Ruby, Tell us how do
you use technology?

[Ruby:] Technology is a tool
that we use in several ways

for communication with others to
e-mail, for conducting research,

using the internet, proving papers,

and preparing electronic
presentations of our work

and for participating and
problem solving on the projects

such as NASA Connect to the
re-emplace where we are going to

[inaudible] and the all our
component for this show,

we are learning well goals into
the design, our space graph use,

for planetary observation.

To do this we may our
different instruments used

for observing planetary
services on space.

One of these is


We get to pick out what we think
are the ripe berries to use as well

as the sort of panels required
to run the space craft.

We will also have to consider
the cost and way of the vehicle

as we tried to put together

that that is possible planetary
observer, we can well --

all the vehicles giving
to us in the activities.

[Viviane:] Well Jennifer this team

through Davis Middle School
leave you and our views

with the challenge to assemble
and test their very own

of Mars surveyor in
a cost effective way

that produces the best results.

Viewers can find that
challenge in Norbert's lab

on the NASA Connect website.

See on the web.

>> Let's have the NASA
Langley research center

in Hampton Virginia, and meet

up with some Gorge Washington
University graduate students,

they are using pictures from
the Mars global surveyor

and geometry to survey Mars.

>> How shadows measure a Mars?

>> How is geometry used
to determine the height

of land formation on Mars?

>> Hey guys I wanted to meet


They are graduate students at
Gorge Washington University.

Thus what you have
studying over there?

>> Well with simple geometry on
shadows, we are able to determine

that elevation on Mars surface,

such as a mountain Olympus
that's three times the size

of mount Everest or valley of

[inaudible], which is the
size of the United States.

>> Wow! This is some
pretty large information.

So let me give this try, what you
are telling is the geometry is used

to determine the elevation
of land formations on Mars?

>> Yes, we have certain example
here for you to demonstrate this.

If this is amount on the surface
of Mars, this is the protractor

to measure the angel of the
sun this is a magic ruler

to measure the length
of the shadow.

If this flash light represents
the sun, we know that like here

on earth, sun is directly overhead
at ninety degrees at high noon

and as day goes on it goes
under zero degrees at sunset.

>> So,

[inaudible] what you are telling
me is this model creates a

right triangle?

>> The bottom leg can be
represented by the length

of the shadow which been
get and taking your picture

with the Mars Globus are there.

Now the sun makes an
angle between the

[inaudible] and the bottom leg.

So let's pretend its
mid-afternoon on Mars.

The sun would be at about an
angle of forty-five degrees which

[inaudible] our shadow?

>> It gives us about
seventeen centimeters.

>> Yeah, you get triangle there.

>> Yes, so using our formula,
remembering the tangent

of forty-five degrees is equal
to one which you can find

by scientific calculator
or tangent tables.

We can find the height
of a mountain

to be seventeen centimeters.

So to double check your
answer, we can see that the

[inaudible] is seventeen

>> That's the about
what you calculated,

that's pretty cool Corey.

>> Well I look in Mars through the
telescope and it is definitely red,

but could green slam have once
existed on the red planet.

That's one of the many reasons
NASA Ames Research Centre

in Mountain View California
is studying Mars.

So now let's join research at Chris
McCay with the latest on the Rain


>> I am interested in Mars
and particular life on Mars.

You know that early Mars
history had water, lots of water.

We can see the rivers and
lakes that were formed by


The question is when it had
water, did it have life?

To understand how life might have
survived on cold planet like Mars,

we have to look for --
we go to places on earth

where life is survived in
very cold dry condition,

Mars like conditions.

This is a rock from the Antarctic
dry valleys of Antarctica,

most Mars like place on earth.

In this rock there is life,

but it's hidden inside the rock
just below the surface there is

layer green and these are

[inaudible] lightning and they
are growing inside the rock,

because the rock provides
them the first of moisture

about the same time allowing
enough light to come through.

By studying life forms
in these environments,

we learn about the strategies that
life can use in a cold dry place.

We might apply those strategies
to the search for life on Mars

and maybe we will find the
evidence that there is life there,

when Mars was not too much colder
than the dry valleys of Antarctica.

>> Well, looks like
the sun has shifted,

that's about all we
have time for today.

>> But before we go, Jennifer
and I would love to hear from you

with your comments and ideas.

So why don't you drop us
a line at NASA Connect.

NASA LRC MS, 400 Hampton
Virginia, 23681 or if you are

on the web e-mail us at

>> We would like to thank
everyone who helped us today.

The Virginia Living Museum,
George Washington University,

our NASA Researchers from
NASA Langley Research Center,

NASA Ames Research Center and
NASA Jet Propulsion Laboratory.


[inaudible] and specially
the student

and teachers from Middle School.

Thanks guys.

If you would like a video tape
copy of this NASA Connect show

and the educators
guide lesson plans,

contact for The NASA
Central Operation

of Resources for Educators.

All this information
and more is located

on the NASA connect website.

For the NASA connect series
I am Jennifer Pulley.

>> And I am Van Hughes.

>> See you next time.

>> Its slice of Pizza.


>> What is survey


>> One of the functions of
the Mars level surveyor was

to watch it follow up.

>> How

[inaudible] used to measure?

>> Today we are uses the


>> What's are the angles --

>> To sun to be -- would be at
about an angle forty-five degrees


>> How shadows --

>> Okay,


>> Welcome to NASA Connect.

>> [inaudible]

>> Welcome to NASA Connect.

>> Sorry.

>> And I am van Hughes, today we
are here at the, oh -- Alright.

>> I think I see, wow!